Finding minimal parameterizations of cylindrical image manifolds

Manifold learning has become an important tool to characterize high-dimensional data that vary nonlinearly due to a few parameters. Applications to the analysis of medical imagery and human motion patterns have been successful despite the lack of effective tools to parameterize cyclic data sets. This paper offers an initial approach to this problem, and provides for a minimal parameterization of points that are drawn from cylindrical manifolds - data whose (unknown) generative model includes a cyclic and a non-cyclic parameter. Solving for this special case is important for a number of current, practical applications and provides a start toward a general approach to cyclic manifolds. We offer results on synthetic and real data sets and illustrate an application to de-noising cardiac ultrasound images.